The Mixed Scattering Problem Of Penetrated And Unpenetrated Obstacles

This paper focuses on the mixed acoustic waves scattering problem of penetrated and unpenetrated obstacles.Assume that D1(?)R2 is a bounded region and it is a penetrated obstacle which has smooth boundary.D2(?)R2 is a bounded region too,and it is a unpenetrated obstacles which has the Lipschitz boundary.The boundary(?)D2 has the dissection(?)DD and(?)DI,they satisfy(?)D2 ?(?)DD ?(?)DI.Finally the problem comes down to the mixed boundary value problem:where U =ui+us,ui=eikx.d is the incident wave,us is the unknown scattered wave,and us satisfys Sommerfeld Radiation condition:uniformly in x = x/|x|.Firstly,we talk about the direct scattering problem,using Green's theorem,we have the uniqueness of the solution;we use the method of boundary integral equations to convert above problem to boundary integral equation,then with the help of the Fredholm theory we can obtain the existence of the solution to the primal problem by the existence of solution to boundary integral equation;Secondly,we use the liner sampling method to solve the inverse scattering problem,so we reconstruct the shape of the obstacle of D1 and D2 by a knowledge of the far-field pattern of the scattered field.In the end,numerical example is given to show the practicability of the linear sampling method in this case.